Ohm's Law

What Is Ohm's Law?

Ohm's Law describes the relationship between potential difference, current, and resistance in an electrical conductor.

For an ohmic conductor at constant temperature:

V = IR

where:

• V = potential difference in volts (V)
• I = current in amperes (A)
• R = resistance in ohms (Ω)

Ohm's Law tells us that, when resistance remains constant:

V ∝ I

If the voltage across an ohmic conductor doubles, the current also doubles.

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Voltage, Current and Resistance

To use Ohm's Law effectively, it is important to understand the three quantities involved.

Voltage

Potential difference, commonly called voltage, is the energy transferred per unit charge between two points.

Unit:

volt (V)

Current

Electric current is the rate of flow of electric charge.

Unit:

ampere (A)

Resistance

Resistance measures how strongly a component opposes the flow of electric current.

Unit:

ohm (Ω)

Ohm's Law connects all three quantities.

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Rearranging Ohm's Law

Starting with:

V = IR

we can rearrange it depending on which quantity we need.

To calculate current:

I = V/R

To calculate resistance:

R = V/I

These three equations should be familiar:

V = IR

I = V/R

R = V/I

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Choosing the Correct Equation

A useful strategy is:

1. Write down the known values.
2. Identify the unknown.
3. Select the appropriate form of Ohm's Law.
4. Substitute values with units.
5. Calculate.
6. Check whether the answer is reasonable.

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Calculating Voltage

A resistor has:

I = 2 A

R = 6 Ω

Calculate the voltage.

Use:

V = IR

V = 2 × 6

V = 12 V

A potential difference of 12 V is required to produce a current of 2 A through a 6 Ω resistor.

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Calculating Current

A 20 Ω resistor is connected across a 10 V supply.

Calculate the current.

Use:

I = V/R

I = 10/20

I = 0.5 A

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Calculating Resistance

A component has:

V = 12 V

I = 3 A

Calculate its resistance.

Use:

R = V/I

R = 12/3

R = 4 Ω

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Understanding the Relationship

For a fixed resistance:

higher voltage → higher current

For a fixed voltage:

higher resistance → lower current

For example, suppose two resistors are connected separately to a 12 V supply.

For R = 3 Ω:

I = 12/3

I = 4 A

For R = 6 Ω:

I = 12/6

I = 2 A

Doubling the resistance halves the current when voltage remains constant.

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What Is an Ohmic Conductor?

An ohmic conductor is a conductor for which current is directly proportional to potential difference, provided its physical conditions remain constant.

In particular, its temperature should remain approximately constant.

For an ohmic conductor:

V/I = constant

Therefore:

R = constant

A fixed resistor can behave approximately as an ohmic conductor over a suitable range.

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Ohmic and Non-Ohmic Components

Not every electrical component obeys Ohm's Law under all conditions.

An ohmic component has approximately constant resistance.

A non-ohmic component has resistance that changes as conditions change.

Examples of non-ohmic components include:

• filament lamps
• diodes
• thermistors
• light-dependent resistors

Their current-voltage relationships are therefore not simple straight lines under all conditions.

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The Filament Lamp

A filament lamp provides an important example of non-ohmic behavior.

As current passes through the filament:

• electrical energy is transferred
• the filament becomes hotter
• lattice vibrations increase
• resistance increases

Therefore, the resistance is not constant.

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Measuring Ohm's Law Experimentally

A typical experiment uses:

• power supply
• resistor
• ammeter
• voltmeter
• variable resistor
• switch
• connecting wires

The ammeter measures current and is connected in series.

The voltmeter measures potential difference and is connected in parallel across the component.

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Collecting V-I Data

The voltage across a resistor can be changed and the corresponding current measured.

For example:

Calculate V/I:

1/0.20 = 5 Ω

2/0.40 = 5 Ω

3/0.60 = 5 Ω

The ratio remains constant.

Therefore:

R = 5 Ω

This is characteristic of an ohmic conductor.

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Interpreting V-I Graphs

A graph can be used to investigate whether a component obeys Ohm's Law.

However, you must first check which quantity is on each axis.

This is extremely important.

A graph of:

V on the vertical axis and I on the horizontal axis

is not interpreted in exactly the same way as a graph with:

I on the vertical axis and V on the horizontal axis.

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V Against I

If voltage is plotted on the vertical axis and current on the horizontal axis:

gradient = ΔV/ΔI

Since:

R = V/I

the gradient represents:

resistance

Therefore:

steeper V-I graph → greater resistance

For an ohmic conductor, the graph is a straight line through the origin.

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Example: Finding Resistance from a V-I Graph

Suppose a straight-line V-I graph contains the point:

I = 2 A

V = 10 V

Then:

gradient = ΔV/ΔI

gradient = 10/2

gradient = 5 V/A

Since:

1 V/A = 1 Ω

the resistance is:

R = 5 Ω

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I Against V

Sometimes current is placed on the vertical axis and voltage on the horizontal axis.

Then:

gradient = ΔI/ΔV

But:

I/V = 1/R

Therefore:

gradient = 1/R

In this type of graph:

steeper line → lower resistance

This is why you should never memorize simply that "gradient equals resistance" without checking the axes.

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Comparing V-I and I-V Graphs

Always inspect the axis labels before calculating resistance.

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Recognizing an Ohmic Conductor from a Graph

An ohmic conductor produces a straight-line relationship through the origin when temperature remains constant.

This means:

V ∝ I

For example:

if V doubles, I doubles.

if V triples, I triples.

The ratio:

V/I

remains constant.

Therefore, the resistance remains constant.

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Recognizing Non-Ohmic Behavior

If the V-I relationship is curved rather than linear, resistance is changing.

A filament lamp provides a common example.

At low current, the filament is relatively cool.

As current increases:

• temperature increases
• resistance increases
• the graph changes gradient

The component therefore does not behave as a constant-resistance ohmic conductor.

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The Diode

A diode allows current to flow much more easily in one direction than the other.

In the forward direction, little current flows until a sufficient forward voltage is reached. The current can then increase rapidly.

In the reverse direction, very little current normally flows.

A diode clearly does not produce the simple straight-line V-I relationship of an ohmic conductor.

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Ohm's Law in Simple Circuits

Consider a circuit containing:

• a 12 V battery
• a 4 Ω resistor

Assuming the resistor is the only significant resistance:

I = V/R

I = 12/4

I = 3 A

Ohm's Law allows us to predict the current before the circuit is constructed.

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Finding an Unknown Resistance

A resistor carries a current of 0.25 A when connected across 6 V.

Use:

R = V/I

R = 6/0.25

R = 24 Ω

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Unit Conversions

Electrical quantities are often given using prefixes.

Current

1 A = 1000 mA

Therefore:

500 mA = 0.500 A

250 mA = 0.250 A

20 mA = 0.020 A

Resistance

1 kΩ = 1000 Ω

Therefore:

2 kΩ = 2000 Ω

4.7 kΩ = 4700 Ω

Voltage

1 kV = 1000 V

1 mV = 0.001 V

Convert units before substituting into Ohm's Law.

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Worked Example with Milliamperes

A resistor has 9 V across it and carries a current of 30 mA.

Calculate the resistance.

First convert:

30 mA = 0.030 A

Then:

R = V/I

R = 9/0.030

R = 300 Ω

A common mistake would be to substitute 30 directly as though it were 30 A.

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Worked Example with Kilohms

A 2.0 kΩ resistor is connected across 12 V.

Convert:

2.0 kΩ = 2000 Ω

Use:

I = V/R

I = 12/2000

I = 0.006 A

Convert to milliamperes:

I = 6 mA

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Ohm's Law in Series Circuits

In a series circuit, the same current passes through each component.

The total resistance is:

R_total = R₁ + R₂ + R₃ + ...

Suppose two resistors are connected in series:

R₁ = 4 Ω

R₂ = 8 Ω

Then:

R_total = 4 + 8

R_total = 12 Ω

If they are connected to a 24 V supply:

I = V/R

I = 24/12

I = 2 A

The current through each resistor is therefore 2 A.

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Voltage Across Series Resistors

For the previous circuit:

I = 2 A

R₁ = 4 Ω

R₂ = 8 Ω

Voltage across R₁:

V₁ = IR₁

V₁ = 2 × 4

V₁ = 8 V

Voltage across R₂:

V₂ = IR₂

V₂ = 2 × 8

V₂ = 16 V

Check:

V_total = V₁ + V₂

V_total = 8 + 16

V_total = 24 V

The individual voltage drops add to the supply voltage.

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Ohm's Law in Parallel Circuits

In a parallel circuit, each branch has the same potential difference.

Suppose two resistors are connected in parallel across a 12 V supply.

R₁ = 6 Ω

R₂ = 4 Ω

Current through R₁:

I₁ = V/R₁

I₁ = 12/6

I₁ = 2 A

Current through R₂:

I₂ = 12/4

I₂ = 3 A

Total current:

I_total = I₁ + I₂

I_total = 5 A

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Comparing Series and Parallel Circuits

Ohm's Law can be applied to individual components or to an equivalent resistance for the whole circuit.

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Combining Circuit Rules with Ohm's Law

Suppose two resistors are connected in series:

R₁ = 5 Ω

R₂ = 10 Ω

Supply voltage:

V = 30 V

First calculate total resistance:

R_total = 5 + 10

R_total = 15 Ω

Calculate current:

I = 30/15

I = 2 A

Then calculate the voltage across each resistor.

V₁ = 2 × 5

V₁ = 10 V

V₂ = 2 × 10

V₂ = 20 V

Check:

10 V + 20 V = 30 V

The results are consistent.

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Circuit Problem-Solving Strategy

When solving an Ohm's Law circuit problem:

Identify what is known

Write down voltage, current and resistance values.

Convert units

Convert mA to A or kΩ to Ω when necessary.

Identify the circuit structure

Determine whether components are in series or parallel.

Apply circuit rules

For example:

• series → same current
• parallel → same voltage

Use Ohm's Law

Apply:

V = IR

to the whole circuit or an individual component.

Check the result

Ask:

• Are the units correct?
• Is the current reasonable?
• Do voltage drops add correctly?
• Do branch currents add correctly?

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Ohm's Law and Electrical Power

Ohm's Law can also be combined with:

P = VI

Since:

V = IR

we can substitute to obtain:

P = I²R

We can also use:

I = V/R

to obtain:

P = V²/R

Therefore:

P = VI

P = I²R

P = V²/R

These relationships are useful when analyzing resistors and electrical heating.

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Example with Power

A 10 Ω resistor carries a current of 2 A.

Voltage:

V = IR

V = 2 × 10

V = 20 V

Power:

P = VI

P = 20 × 2

P = 40 W

Alternatively:

P = I²R

P = 2² × 10

P = 4 × 10

P = 40 W

Both methods give the same result.

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Why Temperature Matters

Ohm's Law is often stated more precisely as:

The current through an ohmic conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant.

This condition matters because resistance can change with temperature.

For most metals:

temperature increases → resistance increases

If the resistance changes, V and I are no longer proportional with the same constant of proportionality.

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Microscopic Explanation

In a metal, free electrons move through a lattice of positive ions.

An applied electric field produces an overall drift of electrons.

The electrons interact with the lattice as they move.

These interactions produce resistance.

For an ohmic conductor at approximately constant temperature, the physical conditions remain sufficiently stable that the resistance remains approximately constant.

This produces the linear relationship:

V ∝ I

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Real-World Applications

Ohm's Law is fundamental to electrical and electronic design.

It can be used when:

• selecting resistors
• designing LED circuits
• analyzing household appliances
• troubleshooting circuits
• determining safe currents
• designing sensors
• calculating voltage drops
• testing electrical components

For example, electronic circuits frequently use resistors to limit current so that sensitive components are not damaged.

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Common Mistakes

Mistake: Mixing up the equations.
Remember that all three come from V = IR.

Mistake: Using milliamperes as amperes.
Convert mA to A before calculating unless the units are being handled consistently.

Mistake: Using kilohms as ohms.
For example, 3 kΩ = 3000 Ω.

Mistake: Assuming every component obeys Ohm's Law.
Filament lamps, diodes and thermistors are common non-ohmic examples.

Mistake: Saying Ohm's Law always applies to a metal regardless of temperature.
The relationship requires constant physical conditions.

Mistake: Assuming the gradient of every V-I graph is resistance.
Check the axes. If V is vertical, gradient = R. If I is vertical, gradient = 1/R.

Mistake: Connecting an ammeter in parallel.
An ammeter should normally be connected in series.

Mistake: Connecting a voltmeter in series.
A voltmeter should be connected in parallel across the component.

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Key Terms

Ohm's Law — relationship between voltage, current and resistance for an ohmic conductor under constant physical conditions.

Potential difference — energy transferred per unit charge, measured in volts.

Voltage — commonly used name for potential difference.

Current — rate of flow of electric charge, measured in amperes.

Resistance — opposition to electric current, measured in ohms.

Ohm (Ω) — SI unit of electrical resistance.

Ohmic conductor — conductor for which current is directly proportional to voltage under constant physical conditions.

Non-ohmic component — component whose resistance is not constant as voltage or current changes.

V-I characteristic — relationship between voltage and current for a component.

Gradient — change in the vertical quantity divided by change in the horizontal quantity.

Ammeter — instrument used to measure current.

Voltmeter — instrument used to measure potential difference.

Series circuit — circuit in which components share a single current path.

Parallel circuit — circuit containing multiple branches.

Voltage drop — potential difference across a circuit component.

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Key Takeaways

• Ohm's Law relates voltage, current and resistance.
• For an ohmic conductor under constant physical conditions, V = IR.
• Voltage is measured in volts, current in amperes and resistance in ohms.
• The equation can be rearranged as I = V/R and R = V/I.
• For constant resistance, increasing voltage increases current proportionally.
• For constant voltage, increasing resistance decreases current.
• An ohmic conductor has approximately constant resistance.
• A straight-line V-I relationship through the origin indicates ohmic behavior.
• If V is plotted vertically against I, the gradient equals resistance.
• If I is plotted vertically against V, the gradient equals 1/R.
• Always inspect graph axes before interpreting gradient.
• Filament lamps, diodes and thermistors can show non-ohmic behavior.
• Ammeters are connected in series.
• Voltmeters are connected in parallel.
• In a series circuit, current is the same through each component.
• In a parallel circuit, voltage is the same across each branch.
• Ohm's Law can be combined with series and parallel circuit rules.
• Unit conversions such as mA to A and kΩ to Ω are essential.
• Ohm's Law can also be combined with electrical power equations.
• The law is widely used in circuit design, testing and troubleshooting.

Check Your Understanding

1. State Ohm's Law.
2. State the units of voltage, current and resistance.
3. A 6 Ω resistor carries 2 A. Calculate the voltage across it.
4. A 12 V supply is connected across a 4 Ω resistor. Calculate the current.
5. A component has 9 V across it and carries 0.3 A. Calculate its resistance.
6. A 15 Ω resistor carries 200 mA. Calculate the voltage across it.
7. A 2 kΩ resistor is connected across 10 V. Calculate the current in amperes and milliamperes.
8. What does it mean for a conductor to be ohmic?
9. Why should temperature remain constant when testing Ohm's Law?
10. Describe the V-I graph of an ohmic conductor.
11. A V-I graph contains the point I = 0.5 A, V = 4 V. Calculate the resistance.
12. Why must you check the axes before using the gradient of a voltage-current graph?
13. Explain why a filament lamp is non-ohmic.
14. Explain why a diode does not have a straight-line V-I characteristic.
15. Two resistors of 4 Ω and 8 Ω are connected in series across 24 V. Calculate the circuit current.
16. For the circuit in Question 15, calculate the voltage across each resistor.
17. Two resistors of 6 Ω and 3 Ω are connected in parallel across 12 V. Calculate the current through each branch.
18. Calculate the total current supplied to the parallel circuit in Question 17.
19. Explain how an ammeter and voltmeter should be connected when investigating Ohm's Law.
20. Explain how Ohm's Law can be used to determine whether an experimental component behaves as an ohmic conductor.